Question

Подскажите пожалуйста люди добрые

Answer 1

Ответ:

$\dfrac{5}{6};$

$1;$

Пошаговое объяснение:

$0,8333...=0,8(3)=\dfrac{83-8}{90}=\dfrac{75}{90}=\dfrac{25}{30}=\dfrac{5}{6};$

$0,4(6)=\dfrac{46-4}{90}=\dfrac{42}{90}=\dfrac{14}{30}=\dfrac{7}{15};$

$0,41(6)=\dfrac{416-41}{900}=\dfrac{375}{900}=\dfrac{125}{300}=\dfrac{25}{60}=\dfrac{5}{12};$

$\dfrac{\dfrac{5}{6}-\dfrac{7}{15}}{1\dfrac{5}{6}} \cdot \dfrac{1,125+1,75-\dfrac{5}{12}}{0,59}=\dfrac{\dfrac{25}{30}-\dfrac{14}{30}}{\dfrac{11}{6}} \cdot \dfrac{2,875-\dfrac{5}{12}}{0,59}=\dfrac{\dfrac{11}{30}}{\dfrac{11}{6}} \cdot \dfrac{\dfrac{23}{8}-\dfrac{5}{12}}{0,59}=$

$=\dfrac{6}{30} \cdot \dfrac{\dfrac{69}{24}-\dfrac{10}{24}}{0,59}=\dfrac{1}{5} \cdot \dfrac{\dfrac{59}{24}}{\dfrac{59}{100}}=\dfrac{1}{5} \cdot \dfrac{59 \cdot 100}{24 \cdot 59}=\dfrac{100}{5 \cdot 24}=\dfrac{20}{24}=\dfrac{5}{6};$

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$2,708333...=2,708(3)=2\dfrac{7083-708}{9000}=2\dfrac{6375}{9000}=2\dfrac{2125}{3000}=2\dfrac{425}{600}=2\dfrac{85}{120}=$

$=2\dfrac{17}{24};$

$0,7(6)=\dfrac{76-7}{90}=\dfrac{69}{90}=\dfrac{23}{30};$

$0,(36)=\dfrac{36}{99}=\dfrac{12}{33}=\dfrac{4}{11};$

$\dfrac{\bigg (\dfrac{5}{8}+2\dfrac{17}{24} \bigg ):2,5}{\bigg (1,3+\dfrac{23}{30}+\dfrac{4}{11} \bigg ) \cdot \dfrac{110}{401}} \cdot \dfrac{1}{2}=\dfrac{\bigg (\dfrac{15}{24}+2\dfrac{17}{24} \bigg ):2,5}{\bigg (\dfrac{13}{10}+\dfrac{23}{30}+\dfrac{4}{11} \bigg ) \cdot \dfrac{110}{401}} \cdot \dfrac{1}{2}=$

$=\dfrac{2\dfrac{32}{24}:2,5}{\dfrac{13 \cdot 3 \cdot 11+23 \cdot 11+4 \cdot 30}{30 \cdot 11}\cdot \dfrac{110}{401}} \cdot \dfrac{1}{2}=\dfrac{2\dfrac{4}{3}:\dfrac{5}{2}}{\dfrac{(39+23) \cdot 11+120}{330} \cdot \dfrac{110}{401}} \cdot \dfrac{1}{2}=$

$=\dfrac{\dfrac{10}{3} \cdot \dfrac{2}{5}}{\dfrac{62 \cdot 11+120}{3} \cdot \dfrac{1}{401}} \cdot \dfrac{1}{2}=\dfrac{\dfrac{4}{3}}{\dfrac{620+62+120}{3 \cdot 401}} \cdot \dfrac{1}{2}=\dfrac{\dfrac{4}{3} \cdot \dfrac{1}{2}}{\dfrac{802}{3 \cdot 401}}=\dfrac{\dfrac{4}{6}}{\dfrac{2}{3}}=\dfrac{\dfrac{2}{3}}{\dfrac{2}{3}}=1;$